This is my understanding so far: eCash tokens are stored locally, but the mint stores the information for each token if it has been already spent or not. Otherwise double spends would be possible.

Regarding restoration I don't know the technical details, but I assume there is some kind of algorithm for deterministically generating eCash tokens from the seed (similar to how key derivation in onchain bitcoin works). However for each derived token, your wallet has to query the mint about whether it has already been spent or not. So I don't think completely offline restoration of eCash is possible.